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The range of integers that can be represented by an $n$ bit $2’s$ complement number system is:

1. $-2^{n-1} \text{ to } (2^{n-1} -1)$

2. $-(2^{n-1} -1) \text{ to } (2^{n-1} -1)$

3. $-2^{n-1} \text{ to } 2^{n-1}$

4. $-(2^{n-1} +1) \text{ to } (2^{n-1} -1)$

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An n-bit two's-complement numeral system can represent every integer in the range −(2n − 1) to +(2n − 1 − 1).

while ones' complement can only represent integers in the range −(2n − 1 − 1) to +(2n − 1 − 1).

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option a by Boss (34.9k points)
Total number of distinct numbers that can be represented using $n$ bits $=2^n.$

In case of unsigned numbers these corresponds to numbers from $0$ to $2^n -1.$

In case of signed numbers in $1's$ complement or sign magnitude representation, these corresponds to numbers from $-(2^{n-1}-1)$ to $2^{n-1}-1$ with $2$ separate representations for $0.$

In case of signed numbers in $2's$ complement representation, these corresponds to numbers from $-2^{n-1}$ to $2^{n-1}-1$ with a single representation for $0.$
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